Deep generative models (DGMs) have achieved remarkable advances. Semi-supervised variational auto-encoders (SVAE) as a classical DGM offers a principled framework to effective generalize from small labelled data to large unlabelled ones, but it is difficult to incorporate rich unstructured relationships within the multiple heterogeneous entities. In this paper, to deal with the problem, we present a semi-supervised co-embedding model for attributed networks (SCAN) based on the generalized SVAE for the heterogeneous data, which collaboratively learns low- dimensional vector representations of both nodes and attributes for partially labelled attributed networks semi-supervisedly. The node and attribute embeddings obtained in a unified manner by our SCAN can benefit not only for capturing the proximities between nodes but also the affinities between nodes and attributes. Moreover, our model also trains a discriminative network to learn the label predictive distribution of nodes. Experimental results on real-world networks demonstrate that our model yields excellent performance in a number of applications such as attribute inference, user profiling and node classification compared to the state-of-the-art baselines.